int main()
{
slong iter;
flint_rand_t state;
flint_printf("pow_acb_series....");
fflush(stdout);
flint_randinit(state);
/* compare with exp/log */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong prec, trunc;
acb_poly_t f, g, h1, h2;
acb_t c;
prec = 2 + n_randint(state, 200);
trunc = n_randint(state, 20);
acb_poly_init(f);
acb_poly_init(g);
acb_poly_init(h1);
acb_poly_init(h2);
acb_init(c);
/* generate binomials */
if (n_randint(state, 20) == 0)
{
acb_randtest(c, state, prec, 10);
acb_poly_set_coeff_acb(f, 0, c);
acb_randtest(c, state, prec, 10);
acb_poly_set_coeff_acb(f, 1 + n_randint(state, 20), c);
}
else
{
acb_poly_randtest(f, state, 1 + n_randint(state, 20), prec, 10);
}
acb_poly_randtest(h1, state, 1 + n_randint(state, 20), prec, 10);
acb_randtest(c, state, prec, 10);
acb_poly_set_acb(g, c);
/* f^c */
acb_poly_pow_acb_series(h1, f, c, trunc, prec);
/* f^c = exp(c*log(f)) */
acb_poly_log_series(h2, f, trunc, prec);
acb_poly_mullow(h2, h2, g, trunc, prec);
acb_poly_exp_series(h2, h2, trunc, prec);
if (!acb_poly_overlaps(h1, h2))
{
flint_printf("FAIL\n\n");
flint_printf("prec = %wd\n", prec);
flint_printf("trunc = %wd\n", trunc);
flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n");
flint_printf("c = "); acb_printd(c, 15); flint_printf("\n\n");
flint_printf("h1 = "); acb_poly_printd(h1, 15); flint_printf("\n\n");
flint_printf("h2 = "); acb_poly_printd(h2, 15); flint_printf("\n\n");
abort();
}
acb_poly_pow_acb_series(f, f, c, trunc, prec);
if (!acb_poly_overlaps(f, h1))
{
flint_printf("FAIL (aliasing)\n\n");
abort();
}
acb_poly_clear(f);
acb_poly_clear(g);
acb_poly_clear(h1);
acb_poly_clear(h2);
acb_clear(c);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("gamma_upper_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
slong m, n1, n2, bits1, bits2, bits3;
acb_poly_t S, A, B, C;
acb_t s, t, c;
int regularized;
regularized = n_randint(state, 3);
bits1 = 2 + n_randint(state, 200);
bits2 = 2 + n_randint(state, 200);
bits3 = 2 + n_randint(state, 200);
m = 1 + n_randint(state, 10);
n1 = 1 + n_randint(state, 10);
n2 = 1 + n_randint(state, 10);
acb_poly_init(S);
acb_poly_init(A);
acb_poly_init(B);
acb_poly_init(C);
acb_init(s);
acb_init(t);
acb_init(c);
acb_poly_randtest(S, state, m, bits1, 3);
acb_poly_randtest(A, state, m, bits1, 3);
acb_poly_randtest(B, state, m, bits1, 3);
acb_randtest(s, state, bits1, 3);
acb_hypgeom_gamma_upper_series(A, s, S, regularized, n1, bits2);
acb_hypgeom_gamma_upper_series(B, s, S, regularized, n2, bits3);
acb_poly_set(C, A);
acb_poly_truncate(C, FLINT_MIN(n1, n2));
acb_poly_truncate(B, FLINT_MIN(n1, n2));
if (!acb_poly_overlaps(B, C))
{
flint_printf("FAIL (consistency)\n\n");
flint_printf("regularized = %d\n\n", regularized);
flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n");
flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n");
flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n");
flint_printf("C = "); acb_poly_printd(C, 15); flint_printf("\n\n");
flint_abort();
}
/* f(h(x)) = -exp(-h(x)) h(x)^(s-1) */
acb_poly_neg(C, S);
acb_poly_exp_series(C, C, n1, bits2);
acb_sub_ui(t, s, 1, bits2);
acb_poly_pow_acb_series(B, S, t, n1, bits2);
acb_poly_mullow(C, C, B, n1, bits2);
acb_poly_neg(C, C);
if (regularized == 0)
{
/* integral(f(h(x)) h'(x))' = f(h(x)) h'(x) */
acb_poly_derivative(B, S, bits2);
acb_poly_mullow(C, C, B, n1, bits2);
acb_poly_truncate(C, n1 - 1);
}
else if (regularized == 1)
{
/* (integral(f(h(x)) h'(x)) / c)' = (f(h(x)) h'(x)) / c */
acb_poly_derivative(B, S, bits2);
acb_poly_mullow(C, C, B, n1, bits2);
acb_gamma(c, s, bits2);
acb_poly_scalar_div(C, C, c, bits2);
acb_poly_truncate(C, n1 - 1);
}
else if (regularized == 2)
{
/* (h(x)^-s integral(f(h(x)) h'(x)))' =
* h(x)^-(s+1) (h(x) f(h(x)) - s integral(f(h(x)) h'(x))) h'(x) */
acb_poly_t D;
acb_poly_init(D);
acb_poly_derivative(B, S, bits2);
acb_poly_mullow(D, C, B, n1, bits2);
acb_poly_integral(D, D, bits2);
acb_poly_scalar_mul(D, D, s, bits2);
acb_poly_mullow(C, C, S, n1, bits2);
acb_poly_sub(D, C, D, bits2);
acb_add_ui(t, s, 1, bits2);
acb_neg(t, t);
acb_poly_pow_acb_series(B, S, t, n1, bits2);
acb_poly_mullow(C, D, B, n1, bits2);
acb_poly_derivative(B, S, bits2);
acb_poly_mullow(C, C, B, n1, bits2);
acb_poly_truncate(C, n1 - 1);
acb_poly_clear(D);
}
acb_poly_derivative(B, A, bits2);
if (!acb_poly_overlaps(B, C))
{
flint_printf("FAIL (derivative)\n\n");
flint_printf("regularized = %d\n\n", regularized);
flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n");
flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n");
flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n");
flint_printf("C = "); acb_poly_printd(C, 15); flint_printf("\n\n");
flint_abort();
}
acb_hypgeom_gamma_upper_series(S, s, S, regularized, n1, bits2);
if (!acb_poly_overlaps(A, S))
{
flint_printf("FAIL (aliasing)\n\n");
flint_printf("regularized = %d\n\n", regularized);
flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n");
flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n");
flint_abort();
}
acb_poly_clear(S);
acb_poly_clear(A);
acb_poly_clear(B);
acb_poly_clear(C);
acb_clear(s);
acb_clear(t);
acb_clear(c);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
